Timeline for Varieties with disjoint prime divisors
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| S Jul 28, 2023 at 19:40 | history | bounty ended | locallito | ||
| S Jul 28, 2023 at 19:40 | history | notice removed | locallito | ||
| Jul 28, 2023 at 19:40 | vote | accept | locallito | ||
| Jul 28, 2023 at 19:35 | vote | accept | locallito | ||
| Jul 28, 2023 at 19:40 | |||||
| Jul 25, 2023 at 11:20 | answer | added | Francesco Polizzi | timeline score: 4 | |
| S Jul 22, 2023 at 3:53 | history | bounty started | locallito | ||
| S Jul 22, 2023 at 3:53 | history | notice added | locallito | Improve details | |
| Jul 19, 2023 at 16:01 | comment | added | abx | The lines are not even cohomogically equivalent, otherwise that would contradict Totaro's paper. And for a smooth threefold $X$ in $\Bbb{P}^4$, $\operatorname{Pic}(X)=\mathbb{Z} $ so every pair of divisors intersect. | |
| Jul 19, 2023 at 14:49 | comment | added | locallito | @abx oh, Im curious about that... some reference or example? That lines are linearly equivalent or something else? Is the same true for 3-folds in P^4 for example? That is something that I did not consider. | |
| Jul 19, 2023 at 13:57 | comment | added | abx | locallito: of course not! A smooth surface of degree $d$ in $\Bbb{P}^3$ is of general type as soon as $d\geq 5$ (and not ruled as soon as $d\geq 3$). | |
| Jul 19, 2023 at 13:36 | comment | added | locallito | @JasonStarr oh! That is just to introduce the topic. Precisely Im asking for "non-trivial" examples where the meaning of "non-trivial" is written above. | |
| Jul 19, 2023 at 13:33 | comment | added | locallito | @abx Is not that a ruled surface? | |
| Jul 19, 2023 at 10:17 | comment | added | Jason Starr | To the OP: please clarify what you are asking about. Presumably those authors explain what they mean by "asymptotically many" disjoint divisors (perhaps bigger than the second Betti number, or some other number defined in terms of invariants of the variety). However, the MO community does not know what you mean by "asymptotically many" disjoint divisors. | |
| Jul 19, 2023 at 4:16 | comment | added | abx | A smooth surface in $\Bbb{P}^3$ can contain many disjoint lines. | |
| Jul 19, 2023 at 3:57 | history | edited | locallito | CC BY-SA 4.0 |
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| Jul 18, 2023 at 23:37 | history | edited | locallito | CC BY-SA 4.0 |
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| Jul 18, 2023 at 23:29 | history | edited | locallito | CC BY-SA 4.0 |
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| S Jul 18, 2023 at 23:14 | review | First questions | |||
| Jul 19, 2023 at 1:43 | |||||
| S Jul 18, 2023 at 23:14 | history | asked | locallito | CC BY-SA 4.0 |